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We provide a road towards obtaining gravitational waveforms from inspiraling material binaries with an accuracy viable for third-generation gravitational wave detectors, without necessarily advancing computational hardware or massively-parallel software infrastructure. We demonstrate a proof-of-principle 1+1-dimensional numerical implementation that exhibits up to 7th-order convergence for highly dynamic barotropic stars in curved spacetime, and numerical errors up to 6 orders of magnitude smaller than a standard method. Aside from high-order interpolation errors (Runges phenomenon), there are no obvious fundamental obstacles to obtaining convergence of even higher order. The implementation uses a novel surface-tracking method, where the surface is evolved and high-order accurate boundary conditions are imposed there. Computational memory does not need to be allocated to fluid variables in the vacuum region of spacetime. We anticipate the application of this new method to full $3! +! 1$-dimensional simulations of the inspiral phase of compact binary systems with at least one material body. The additional challenge of a deformable surface must be addressed in multiple spatial dimensions, but it is also an opportunity to input more precise surface tension physics.
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The non
We have studied the dynamics of an equal-mass magnetized neutron-star binary within a resistive magnetohydrodynamic (RMHD) approach in which the highly conducting stellar interior is matched to an electrovacuum exterior. Because our analysis is aimed
The dynamics of self-gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations. The break-down of well-posedness on the fluid-vacuum interface remains a challenging open problem, which is manifested in simul
We investigate the tidal deformability of a superfluid neutron star. We calculate the equilibrium structure in the general relativistic two-fluid formalism with entrainment effect where we take neutron superfluid as one fluid and the other fluid is c
We present the first numerical solutions of the causal, stable relativistic Navier-Stokes equations as formulated by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). For this initial investigation we restrict to plane-symmetric configurations of a conf